All categories

2 years ago

The first term of an arithmetic sequence is 4 and the tenth term is 67.

Mathematics

1 answer:

serg [7]2 years ago

8 0

Answer:

d = 7

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Give a₁₀ = 67 and a₁ = 4 , then

a₁ + 9d = 67

4 + 9d = 67 ( subtract 4 from both sides )

9d = 63 ( divide both sides by 9 )

d = 7

You might be interested in

The diagonal of a rectangle is of length a. It splits each corner forming two angles with a ratio of 1:2. The area of the rectan

HACTEHA [7]

Answer:

Step-by-step explanation:

Given

Length of diagonal is a

Diagonal divides the angle in 1:2

such that $\theta +2\theta =90$ (because angle between two sides is 90)

$3\theta =90$

$\theta =30^{\circ}$

width of rectangle is $b=a\sin \theta =\frac{a}{2}$

Length of rectangle is $L=a\cos 30=\frac{\sqrt{3}}{2}a$

Area of rectangle $A=L\cdot b$

$A=\frac{\sqrt{3}}{2}a\times \frac{a}{2}$

$A=\frac{\sqrt{3}}{4}a^2$

5 0

2 years ago

Footballs cost $22.00 each. The athletic director has $277.00 in his budget to spend on footballs there is a $13.00 shipping fee

ZanzabumX [31]

Answer:

Step-by-step explanation:

x = number of footballs he can order

22*x + 13 (shipping fee) = 277

22x = 264 Subtract 13 from both sides

x = 16 Divide both sides by 22

Our solution is 16 footballs

5 0

3 years ago

The hypotenuse of a right triangle is twice the length of one of its legs. Th length of the other leg is three feet. Find the le

shutvik [7]

Step-by-step explanation:

go for it this is your questions answer

3 0

3 years ago

How do you write the algebraic expression: x=-2.5 like i mean the answer

Ganezh [65]

Answer:

2.5 × t = 2.5 t

Step-by-step explanation:

5 0

2 years ago

The polynomial p(x)=x^3-6x^2+32p(x)=x 3 −6x 2 +32p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 6, x, squar

Ray Of Light [21]

Answer:

(x-4)(x-4)(x+2)

Step-by-step explanation:

Given p(x) = x^3-6x^2+32 when it is divided by x - 4, the quotient gives

x^2-2x-8

Q(x) = P(x)/d(x)

x^3-6x^2+32/x- 4 = x^2-2x-8

Factorizing the quotient

x^2-2x-8

x^2-4x+2x-8

x(x-4)+2(x-4)

(x-4)(x+2)

Hence the polynomial as a product if linear terms is (x-4)(x-4)(x+2)

8 0

2 years ago